Mclaurin's series

I am given $\displaystyle y=f(x)=tan(2tan^{-1}x+\frac{\pi}{4})$ for [ltex]-0.4<=x<=0.4[/tex] and asked to expand this using mclaurin's series which gives $\displaystyle g(x)=1+4x+8x^2+20x^3+...$
I was then asked to find the range of values of $\displaystyle x$ for which the values of $\displaystyle g(x)$ differs from $\displaystyle f(x)$ by less than $\displaystyle 0.5$